US7715636B2 - Decoding apparatus, dequantizing method, distribution determining method, and program thereof - Google Patents

Decoding apparatus, dequantizing method, distribution determining method, and program thereof Download PDF

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US7715636B2
US7715636B2 US11/179,988 US17998805A US7715636B2 US 7715636 B2 US7715636 B2 US 7715636B2 US 17998805 A US17998805 A US 17998805A US 7715636 B2 US7715636 B2 US 7715636B2
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Shunichi Kimura
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Fujifilm Business Innovation Corp
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
    • H04N19/124—Quantisation
    • H04N19/126—Details of normalisation or weighting functions, e.g. normalisation matrices or variable uniform quantisers
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/44—Decoders specially adapted therefor, e.g. video decoders which are asymmetric with respect to the encoder

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  • the invention relates to a decoding apparatus for decoding code data generated by an encoding process. More specifically, the invention relates to a decoding apparatus for dequantize code data generated by an encoding process including quantizing data, to decode the code data.
  • the lossy coding process causes coding distortion; this is a problem.
  • the JPEG process has a problem in that block distortion occurs at DCT block boundaries of decoded images (coding distortion).
  • FIGS. 1A and 1B are block diagrams schematically illustrating a transform coding method such as JPEG and JPEG2000, where FIG. 1A shows an outline of an encoding process and FIG. 1B shows an outline of a decoding process.
  • FIGS. 2A to 2C are diagrams illustrating a quantization process in the transform coding method.
  • a transform coefficient T(c, i, j) and a quantization index Q(c, i, j) shown in FIGS. 1A and 1B are functions of variables c, i and j.
  • the variable c is an index indicating a kind of transform coefficient. For example, in the case of the DCT transform using 8 ⁇ 8 blocks, the variable c is a value (an integer in a range of 1 to 64) indicating one of 64 (8 ⁇ 8) transform coefficients.
  • the variable c is a value indicating one of components such as 1 HH, 1 LH, 1 HL, 2 HH, 2 LH, 2 HL, . . . , NLL.
  • the transform variables i and j are variables indicating positions of the transform coefficients, respectively.
  • T (c, i, j) a c-th transform coefficient in a block located at an i-th row from the top and a j-th column from the left.
  • T (c, i, j) data of a c-th transform coefficient located at an i-th row from the top and a j-th column from the left.
  • an input image G is subject to a transform process such as the discrete cosine transform (DCT) or the wavelet transform to generate a transform coefficient T of the input image G.
  • the transform coefficient T is then quantized into a quantization index Q.
  • the quantization index Q is subject to an entropy coding process (lossless coding process) to be a compression code F.
  • the quantization index refers to information used to distinguish quantization values.
  • the quantization value refers to a value to which a group of numerical values within a specific range (quantization interval) are degenerated.
  • the quantization values are discrete values ( ⁇ 2 ⁇ D(c) to 2 ⁇ D(c) in this example) representing quantization intervals (A- 2 ⁇ A 2 ), respectively.
  • Code data (the compression code F) generated in this way are entropy-decoded into a quantization index Q, as shown in FIG. 1B .
  • This quantization index Q is equivalent to the quantization index Q in the encoding process.
  • the quantization index Q is dequantized into a transform coefficient R (i.e., a dequantization value). Thereafter, the transform coefficient R is inversely transformed to generate a decoded image H.
  • a transform coefficient R i.e., a dequantization value
  • the dequantization value refers to a value, which is generated based on the quantization index or the quantization value and is used for decoding of data.
  • the dequantization value is a transform coefficient of the JPEG or JPEG2000 (transform coefficient being associated with a quantization index).
  • coding distortion occurs during the quantization.
  • precision of the transform coefficient T of an original image is higher than that of the quantization index Q. Accordingly, the transform coefficient R reproduced by using the quantization index Q may be different from the original transform coefficient T. This is the cause of the coding distortion.
  • the quantization is performed using a quantization step width D(c) prepared for each transform coefficient c.
  • the quantization step width D(c) is a function of the kind of transform coefficient c.
  • the quantization index Q is calculated according to the following equation in the quantization.
  • Q ( c, i, j ) round( T ( c, i, j )/ D ( c ))
  • round ( ) is a function outputting an integer closest to an input value.
  • the dequantization value R is calculated according to the following equation in the dequantization.
  • R ( c, i, j ) Q ( c, i, j ) ⁇ D ( c )
  • the quantization index Q and the dequantization value R are calculated according to the following equations.
  • Q ( c, i, j ) sign( T ( c, i, j )) ⁇ floor(
  • R ( c, i, j ) ( Q ( c, i, j )+ r ) ⁇ D ( c )
  • R ( c, i, j ) ( Q ( c, i, j ) ⁇ r ) ⁇ D ( c )
  • Q ( c, i, j ) 0
  • Q ( c, i, j ) 0
  • signal( ) is a function outputting positive sign or negative sign
  • floor( ) is a function nulling decimal places
  • is a symbol representing an absolute value
  • JPEG2000 there may be a case where lower bits are not encoded. Here, a case where all bits including the least significant bit are encoded will be described by way of examples.
  • JPEG2000 it is possible to obtain number of bits, which are not encoded in the encoding, from a code stream in the decoding. Accordingly, by shifting the quantization step width D to the left by the number of bits and setting the shifted quantization step width as a new quantization width, the JPEG2000 may have the same operation as the JPEG.
  • transform coefficients T (before the quantization) generated by the transform process performed for the input image G are distributed on an X axis, which is a numerical straight line.
  • the quantization index Q becomes 0 by the quantization process. Similarly, if a transform coefficient T exists in a quantization interval Aq, the quantization index Q becomes q.
  • the dequantization value R of 0 is generated by the dequantization process.
  • the dequantization value R of D(c) is generated.
  • the quantization interval Aq has a range of d 1 to d 2 .
  • the transform coefficient T is included in the range of d 1 to d 2 .
  • a dequantization value of the transform coefficient T is R.
  • a transform coefficient for generating a decoded image is the dequantization value R.
  • the transform coefficient T of an original image has any value within the range of d 1 to d 2 and is not always equivalent to the dequantization value R.
  • a difference between the original transform coefficient T and the dequantization value R occurs. This difference is the cause of the coding distortion.
  • the lossy coding process realizes a lossy data compression by degenerating a plurality of data values (original data values existing in each quantization interval) into one quantization value (a quantization value corresponding to each quantization interval), but at the same time, the coding distortion occurs due to the quantization.
  • a parameter for reducing compression efficiency in the encoding process may be selected.
  • a filtering method a decoded image is subject to a low pass filtering process so as to make coding distortion faint and be conspicuous.
  • noise method noises are added to the decoded image or the transformation coefficient so as to make coding distortion faint and be conspicuous.
  • This method makes the coding distortion faint using the low pass filter so that it is difficult for this distortion to be discriminated.
  • the coding distortion is considered to be noticeable when the region is determined to be a flat image region.
  • a decoded image is generated from an encoded image (i.e., a decoding process is performed)
  • a decoding apparatus includes a random-number generating section and a decoding section.
  • the random-number generating section generates random numbers according to distribution of original data corresponding to respective quantization indexes.
  • the decoding section generates decoded data on a basis of the random numbers generated by the random-number generating section.
  • a decoding apparatus includes a standard-deviation acquiring section, a multiplying section, an upper-limit-value acquiring section, and a random-number generating section.
  • the standard-deviation acquiring section acquires a standard deviation of transform coefficients corresponding to quantization indexes.
  • the multiplying section multiplies the standard deviation acquired by the standard-deviation acquiring section by a preset value.
  • the upper-limit-value acquiring section acquires an upper limit value of generated random numbers.
  • the random-number generating section uniformly generates the random numbers, with smaller one of the standard deviation multiplied by the preset value by the multiplying section and the upper limit value acquired by the upper-limit-value acquiring section being an upper limit.
  • a decoding apparatus includes a frequency measuring section, a histogram normalizing section, an addition range determining section, and a distribution determining section.
  • the frequency measuring section measures appearance frequency of quantization indexes.
  • the histogram normalizing section generates normalized histograms based on the appearance frequency measured by the frequency measuring section.
  • the addition range determining section determines an addition range in which frequency distribution of the quantization indexes is added.
  • the distribution determining section determines at least one of a standard deviation and a variance based on the histograms generated by the histogram normalizing section and the addition range determined by the addition range determining section.
  • a decoding apparatus includes a first calculating section, a second calculating section, and a distribution estimating section.
  • the first calculating section calculates at least one of a standard deviation of quantization indexes and a variance of the quantization indexes.
  • the second calculating section calculates at least one of a standard deviation of a Laplace distribution and a variance of the Laplace distribution so that a sum of values of frequency of the quantization indexes within a preset range is equal to an integral value of a Laplace distribution function corresponding to the preset range.
  • the distribution estimating section estimates distribution of original data corresponding to the quantization indexes using at least one of (A) the at least one of the standard deviation and the variance calculated by the first calculating section and (B) the at least one of the standard deviation and the variance calculated by the second calculating section.
  • a dequantizing method includes generating random numbers according to distribution of original data corresponding to respective quantization indexes; and generating dequantization values based on the generated random numbers.
  • a distribution determining method includes adding values of frequency of the respective quantization indexes; and calculating at least one of a variance of a Laplace distribution and a standard deviation of the Laplace distribution so that a resultant value of the addition of values of frequency is equal to an integral value when a Laplace distribution function is integrated so that an integral range of a right side is equal to an integral range of a left side with using a maximum frequency position of the Laplace distribution as a reference.
  • a storage medium which is readable by a computer, stores a program of instructions executable by the computer to perform a dequantization function comprising the steps of generating random numbers according to distribution of original data corresponding to respective quantization indexes; and generating dequantization values based on the generated random numbers.
  • a storage medium which is readable by a computer, stores a program of instructions executable by the computer to perform a dequantization function comprising the steps of adding values of frequency of the respective quantization indexes; and calculating at least one of a variance of a Laplace distribution and a standard deviation of the Laplace distribution so that a resultant value of the addition of values of frequency is equal to an integral value when a Laplace distribution function is integrated so that an integral range of a right side is equal to an integral range of a left side with using a maximum frequency position of the Laplace distribution as a reference.
  • FIG. 1A is a block diagram schematically illustrating an encoding process of a transform coding method such as JPEG and JPEG2000;
  • FIG. 1B is a block diagram schematically illustrating a decoding process of a transform coding method such as JPEG and JPEG2000;
  • FIG. 2A is a diagram illustrating a quantization process in the transform coding method
  • FIG. 2B is a diagram illustrating a quantization process in the transform coding method
  • FIG. 2C is a diagram illustrating a quantization process in the transform coding method
  • FIG. 3 is a diagram illustrating a hardware configuration of a decoding apparatus 2 to which a decoding method according to embodiments of the invention is applied, with providing a controller 20 centrally;
  • FIG. 4 is a diagram illustrating a functional configuration of a decoding program 5 executed by the controller 20 shown in FIG. 3 , for implementing a decoding method according to the embodiments of the invention;
  • FIG. 5 is a diagram illustrating a distribution estimating section 520 ( FIG. 4 ) in more detail
  • FIG. 6 is a diagram illustrating an exemplary histogram h and an exemplary distribution function L (Laplace function);
  • FIG. 7A is a diagram illustrating a distribution estimating process performed by a zero transform coefficient distribution estimating section 526 ;
  • FIG. 7B is a diagram illustrating a distribution estimating process performed by a zero transform coefficient distribution estimating section 526 ;
  • FIG. 8A is a schematic diagram illustrating correction by a correcting section 580 ;
  • FIG. 8B is a schematic diagram illustrating correction by a correcting section 580 ;
  • FIG. 9 is a flow chart of a decoding process S 10 by the decoding program 5 ( FIG. 4 );
  • FIG. 10 is a diagram illustrating an exemplary filter used by a dequantization-value estimating section 500 .
  • FIG. 11A is a diagram illustrating a polygonal-line approximation
  • FIG. 11B is a diagram illustrating a polygonal-line approximation
  • FIG. 11C is a diagram illustrating a polygonal-line approximation
  • FIG. 11D is a diagram illustrating a polygonal-line approximation
  • FIG. 11E is a diagram illustrating a polygonal-line approximation
  • FIG. 12 is a diagram illustrating transform coefficients in the JPEG2000
  • FIG. 13 is a diagram illustrating a distribution estimating section 520 in a second embodiment in more detail
  • FIG. 14 is a graph showing a relationship between the maximum value of quantization values and an optimal N value
  • FIG. 15 is a flow chart of an N value determining process
  • FIG. 16 is a graph showing a ratio of a standard deviation of original transform coefficients to an estimated standard deviation
  • FIG. 17 is a diagram showing a ratio of a standard deviation of original transform coefficients to an estimated standard deviation when a fourth modification is applied.
  • a decoding process to be described in this embodiment is approximately similar to that described in ITU-T Recommendation T.81. However, the decoding process of this embodiment is different in a dequantization process from that of ITU-T Recommendation T.81.
  • FIG. 3 is a diagram illustrating a hardware configuration of the decoding apparatus 2 to which a decoding method according to the invention is applied, with a controller 20 as the central figure.
  • the decoding apparatus 2 includes a controller 20 including CPU 202 , a memory 204 and the like, a communication unit 22 , a storage unit 24 such as HDD, CD and the like, and a user interface unit (UI unit) 26 including an LCD display device or a CRT display device, a keyboard, a touch panel and the like.
  • a controller 20 including CPU 202 , a memory 204 and the like, a communication unit 22 , a storage unit 24 such as HDD, CD and the like, and a user interface unit (UI unit) 26 including an LCD display device or a CRT display device, a keyboard, a touch panel and the like.
  • UI unit user interface unit
  • the decoding apparatus 2 is a general-purpose computer in which a decoding program 5 , which will be described later, is installed.
  • the decoding apparatus 2 acquires code data through the communication unit 22 , the storage unit 24 or the like and decodes the acquired code data.
  • FIG. 4 is a diagram illustrating a functional configuration of the decoding program 5 executed by the controller 20 shown in FIG. 3 , for implementing a decoding method according to embodiments of the invention.
  • the decoding program 5 includes an entropy decoding section 40 , a dequantizing section 50 and an inverse transforming section 60 .
  • the dequantizing section 50 includes a dequantization-value estimating section 500 , a distribution estimating section 520 , an expected-value estimating section 540 , a random-number generating section 560 , a correcting section 580 , and a dequantization-value outputting section 590 .
  • the entropy decoding section 40 entropy-decodes input code data and outputs the decoded data to the dequantizing section 50 .
  • the entropy decoding section 40 of this embodiment decodes the input code data to generate a quantization index Q and outputs the generated quantization index Q to the dequantizing section 50 .
  • the dequantizing section 50 generates a dequantization value R based on the quantization index Q input from the entropy decoding section 40 and outputs the generated dequantization value R to the inverse transforming section 60 .
  • the inverse transforming section 60 performs an inverse transform based on the dequantization value R input from the dequantizing section 50 to generate a decoded image.
  • the dequantization-value estimating section 500 estimates a dequantization value based on the quantization index Q input from the entropy decoding section 40 , and outputs the estimated dequantization value to the correcting section 580 . That is, the dequantization-value estimating section 500 does not always generate a single dequantization value for one quantization index value, but can generate a plurality of different dequantization values for one quantization index value. In other words, although the dequantization-value estimating section 500 generates one dequantization value for each quantization index, the dequantization-value estimating section 500 does not necessarily generate the same dequantization value even when input quantization indexes have the same value.
  • the dequantization-value estimating section 500 of this embodiment calculates a correction factor ⁇ of the dequantization value R corresponding to the quantization index of a given block, based on the quantization index of the given block and the quantization index (limited to one having a quantization index of the same kind c as the transform coefficient) of another block adjacent to the given block, and outputs the calculated correction factor ⁇ to the correcting unit 580 .
  • a correction factor ⁇ corresponding to each transform coefficient kind c and each quantization index q is denoted by ⁇ ycq.
  • ⁇ ycq the number of signals each having the transform coefficient kind c and the quantization index q
  • the distribution estimating section 520 estimates distribution of transform coefficients (of original data) based on a plurality of quantization indexes (or, dequantization values corresponding to the plurality of quantization indexes) input from the entropy decoding section 40 , and then outputs distribution data representing the estimated distribution of transform coefficients to the expected-value estimating section 540 and the random-number generating section 560 .
  • the distribution estimating section 520 in this example calculates the frequency distribution of quantization indexes for each transform coefficient kind c, and then generates the distribution data for each transform coefficient kind c based on the calculated frequency distribution.
  • the expected-value estimating section 540 calculates expected values of the dequantization values based on the distribution data input from the distribution estimating section 520 , and then outputs the calculated expected values and the distribution data to the correcting section 580 .
  • the expected-value estimating section 540 calculates expected values for each quantization interval (that is, expected values for each quantization index value) based on the distribution data generated for each transform coefficient kind c.
  • an expected value is indicated by E( ⁇ Tcq). That is, the expected value E( ⁇ Tcq) indicates estimated expected values of differences between the dequantization values R corresponding to the quantization indexes in a one-to-one manner and the original transform coefficients T corresponding to the quantization indexes.
  • the random-number generating section 560 generates random numbers according to the distribution data input from the distribution estimating section 520 , and outputs the generated random numbers to the dequantization-value outputting section 590 .
  • the correcting section 580 corrects the dequantization value (the correction factor ⁇ of the dequantization value in this example) input from the dequantization-value estimating section 500 based on the distribution data or the expected values input from the expected-value estimating section 540 .
  • the correcting section 580 corrects the dequantization value (the correction factor ⁇ of the dequantization value in this example) input from the dequantization-value estimating section 500 to be in a preset range (for example, in the case of the dequantization value, a quantization interval corresponding to the quantization index), and then outputs the corrected dequantization value (the correction factor ⁇ ) to the dequantization-value outputting section 590 .
  • the correcting section 580 in this example corrects the correction factor ⁇ input from the dequantization-value estimating section 500 based on the expected value input from the expected-value estimating section 540 such that the frequency distribution of quantization indexes calculated by the distribution estimating section 520 becomes approximately identical with the frequency distribution of dequantization values calculated by the dequantization-value estimating section 500 for each transform coefficient kind c and each quantization interval, and then linearly corrects the corrected correction factor ⁇ again to fall within a range of ⁇ 0.5 to 0.5 in the JPEG.
  • the linear correction executed by the correcting section 580 is, for example, achieved by selecting the maximum value ⁇ max and the minimum value ⁇ min from among the correction factors ⁇ corresponding to the same quantization index and then by linearly transforming all the correction factors ⁇ such that the selected maximum value ⁇ max and minimum value ⁇ min fall within the preset range (the range of ⁇ 0.5 to 0.5 in the JPEG).
  • the correcting section 580 may take the correction factors ⁇ as a boundary value of this range (i.e., one of ⁇ 0.5 and 0.5, which is closer to ⁇ ) if the correction factors ⁇ is outside the range of ⁇ 0.5 to 0.5. Also, the correcting section 580 may take the correction factors ⁇ as 0 if the correction factors ⁇ is outside the range of ⁇ 0.5 to 0.5.
  • the dequantization-value outputting section 590 determines a dequantization value to be applied by using the dequantization value (the correction factors ⁇ of the dequantization value in this example) input from the correcting section 580 or the random numbers input from the random-number generating section 560 , and then outputs the determined dequantization value to the inverse transforming section 60 .
  • the decoding program 5 of this embodiment does not apply the random numbers generated by the random-number generating section 560 as the dequantization values themselves, but applies the random numbers generated by the random-number generating section 560 as the correction factors ⁇ of the dequantization values.
  • FIG. 5 is a diagram illustrating a distribution estimating section 520 of FIG. 4 in more detail.
  • the distribution estimating section 520 includes a zero determining section 522 , a non-zero transform coefficient distribution estimating section 524 , and a zero transform coefficient distribution estimating section 526 .
  • the zero determining section 522 classifies the quantization indexes input from the entropy decoding section 40 according to an attribute (for example, the kind of transform coefficients) of original data corresponding to the quantization indexes, and determines as to whether or not the frequency distribution of the original data can be estimated only by groups of quantization indexes classified according to attributes of the original data (in other words, whether or not the frequency distribution can be estimated using correlation between a group of quantization indexes classified according to an attribute of the original data and another group of quantization indexes classified according to a different attribute of the original data).
  • an attribute for example, the kind of transform coefficients
  • the zero determining section 522 in this example determines as to whether the quantization indexes input from the entropy decoding section 40 correspond to zero transform coefficients or non-zero transform coefficients, outputs the quantization indexes determined to correspond to the non-zero transform coefficients to the non-zero transform coefficient distribution estimating section 524 , and instructs the zero transform coefficient distribution estimating section 526 to apply a distribution estimation process to the quantization indexes determined to correspond to the zero transform coefficients, using distribution of the non-zero transform coefficients.
  • the non-zero transform coefficients refer to transform coefficients in which any of the quantization indexes of one transform coefficient kind c is not zero.
  • the zero transform coefficients refer to transform coefficients in which all of the quantization indexes of one transform coefficient kind c are zero. In other words, all transform coefficients other than the zero transform coefficients are the non-zero transform coefficients.
  • the non-zero transform coefficient distribution estimating section 524 estimates the frequency distribution (transform coefficients in this example) of the original data based on the quantization indexes input from the zero determining section 522 .
  • the non-zero transform coefficient distribution estimating section 524 generates the frequency distribution of the groups of quantization indexes having the same attribute (in this example, a plurality of quantization indexes corresponding to the same transform coefficient kind c), and prepares a probability density function of quantization indexes based on the generated frequency distribution of quantization indexes. This probability density function is applied as an approximation to a probability density function of transform coefficients.
  • the non-zero transform coefficient distribution estimating section 524 in this example prepares a histogram hc(q) of the quantization indexes Q(c, i, j) input from the zero determining section 522 (the quantization indexes corresponding to the non-zero transform coefficients) for each transform coefficient kind c.
  • hc ⁇ ( q ) ⁇ i ⁇ ⁇ j ⁇ ht ⁇ ( c , q , i , j ) ( 1 )
  • the non-zero transform coefficient distribution estimating section 524 in this example approximates the prepared histogram hc(q) by the Laplace distribution, taking this Laplace function as a distribution function of transform coefficients T.
  • the non-zero transform coefficient distribution estimating section 524 can obtain the distribution function of transform coefficients T by calculating ⁇ in Equation (2).
  • the non-zero transform coefficient distribution estimating section 524 normalizes the prepared histogram hc (q) with the width D(c) of a quantization interval and the total number of quantization indexes, and transforms the normalized histogram hc(q) into a probability density function fhc(x). Specifically, the non-zero transform coefficient distribution estimating section 524 transforms the histogram hc (q) into the probability density function fhc(x) according to the following equation.
  • the non-zero transform coefficient distribution estimating section 524 calculates the Laplace function approximating the histogram hc(q).
  • FIG. 6 is a diagram illustrating a histogram h and a distribution function L (Laplace function).
  • the non-zero transform coefficient distribution estimating section 524 may find ⁇ to make a difference (an area difference in this example) between the Laplace function L(x) and the histogram fhc(x) as small as possible.
  • error function Err( ⁇ ) is defined as a function to estimate ‘making the difference as small as possible’.
  • This error function Err( ⁇ ) is a function of summing absolute vales of differences of areas of the probability density functions obtained for the quantization index values q. As values of the error function Err( ⁇ ) become small, it can be said that the histogram fhc(x) approaches the Laplace function L(x).
  • the non-zero transform coefficient distribution estimating section 524 obtains ⁇ to minimize the error function Err( ⁇ ) through a numerical calculation.
  • the zero transform coefficient distribution estimating section 526 estimates frequency distribution of zero transform coefficients based on the frequency distribution of other transform coefficients estimated by the non-zero transform coefficient distribution estimating section 524 according to instructions from the zero determining section 522 .
  • the zero transform coefficient distribution estimating section 526 can estimate the frequency distribution only if the histogram has a meaningful shape, but cannot estimate the shape of the frequency distribution when the histogram in which all values of frequency are zero is prepared.
  • the zero transform coefficient distribution estimating section 526 estimates the shape of the Laplace distribution in which all quantization indexes of the transform coefficient kind c are zero, using another obtained distribution data ( ⁇ in this example), according to a method to be described below.
  • transform coefficient kinds are arranged in a two-dimensional 8 ⁇ 8 matrix.
  • values of ⁇ are arranged in a two-dimension, corresponding to (1, 1) to (8, 8) components of DCT coefficients, as shown in FIG. 7A . That is, values of a corresponding to transform coefficients having (x, y) components are represented by ⁇ (x, y).
  • ⁇ (1, 1) is a value of a having a DC component
  • ⁇ (8, 8) is a value of ⁇ of a transform coefficient representing the highest AC component.
  • this value of ⁇ is not used for the estimation of values of ⁇ .
  • ⁇ (x, y) is a function on an x-y plane.
  • the zero transform coefficient distribution estimating section 526 determines this function ⁇ (x, y) using the values of ⁇ already obtained (that is, the values of ⁇ calculated by the non-zero transform coefficient distribution estimating section 524 ) and estimates the values of ⁇ corresponding to the zero transform coefficients.
  • ⁇ (x, y) already obtained is set as ⁇ (x(u), y(u))
  • the zero transform coefficient distribution estimating section 526 can obtain the parameters a, b and C by solving the matrix.
  • the zero transform coefficient distribution estimating section 526 may correct ⁇ (x, y) to monotonously decrease with respect to x and yin order to obtain more pertinent estimation values of ⁇ . That is, when ⁇ (x(v), y(v)) is obtained with assuming that the equation of ⁇ (x (v), y(v)) C exp( ⁇ ax(v) by(v)), ⁇ (x(v), y(v)) is made smaller than or equal to ⁇ (x, y) whose coordinate (x, y) is less than that of ⁇ (x(v), y(v)) Specifically, the zero transform coefficient distribution estimating section 526 makes an correction using the following equation.
  • the random-number generating section 560 applies a variable transformation, according to the quantization indexes Q(c, i, j) to be processed, to the distribution function fc(x) input from the distribution estimating section 520 (that is, the function corresponding to the values of ⁇ (distribution data) calculated by the non-zero transform coefficient distribution estimating section 524 or the zero transform coefficient distribution estimating section 526 ).
  • the random-number generating section 560 generates the following function fcq(x).
  • fcq ⁇ ( x ) ⁇ fc ⁇ ( d ⁇ ⁇ 2 - d ⁇ ⁇ 1 ⁇ max - ⁇ min ⁇ ( x - ⁇ min ) - d ⁇ ⁇ 1 ) ⁇ d ⁇ ⁇ 1 d ⁇ ⁇ 2 ⁇ fc ⁇ ( t ) ⁇ d t ⁇ min ⁇ x ⁇ ⁇ max 0 otherwise ( 6 )
  • This function fcq(x) is a probability density function corresponding to the transform coefficient kind c and the transform coefficients of the quantization indexes q.
  • this probability density function is obtained by transforming the range of d 1 to d 2 into a range of ⁇ min to ⁇ max.
  • the random-number generating section 560 generates random numbers ⁇ , which match the probability density function fcq(x).
  • the random numbers ⁇ are used as correction factors ⁇ for calculation of the dequantization values by the dequantization-value outputting section 590 ( FIG. 4 ).
  • the random-number generating section 560 may generate the random numbers to match the following probability density function fcq(x) and the dequantization-value outputting section 590 may output the random numbers as the dequantization values to the inverse transforming section 60 .
  • fcq ⁇ ( x ) ⁇ fc ⁇ ( x ) ⁇ d ⁇ ⁇ 1 d ⁇ ⁇ 2 ⁇ fc ⁇ ( t ) ⁇ d t d ⁇ ⁇ 1 ⁇ x ⁇ d ⁇ ⁇ 2 0 otherwise ( 7 )
  • a method of generating the random numbers to match the probability density function fcq(x) will be described.
  • a random number generating method for example, an inverse function method, which is disclosed in ‘Knowledge of random number’ (Wakimoto Kazumasa, Morikita Shuppan Co., Ltd., pp. 61-64), may be applied.
  • random numbers X in an interval [0, 1] are generated from a uniform random generator.
  • the function F ⁇ 1 cq (x) may be fixed in a simple form in advance.
  • fcq(x) is normalized in advance.
  • the random-number generating section 560 can generates the random numbers as the correction factors ⁇ appropriate for the distribution of transform coefficients, based on the distribution data input from the distribution estimating section 520 .
  • FIGS. 8A and 8B are schematic diagrams illustrating correction by the correcting section 580 .
  • the correcting section 580 shifts (a 3 ) the distribution of dequantization values to match an estimated expected value (a 1 ) of the transform coefficients T to an expected value (a 2 ) of the dequantization values.
  • the correcting section 580 makes the distribution small toward the expected value of the dequantization values (the correction factors ⁇ ) without moving the expected value (b 2 ).
  • the correcting section 580 makes the above-mentioned correction for the correction factors ⁇ input from the dequantization-value estimating section 500 .
  • FIG. 9 is a flow chart of a decoding process S 10 executed by the decoding program 5 ( FIG. 4 ).
  • the code data (of the JPEG) of image data are input will be described by way of examples.
  • Step S 100 the entropy decoding section 40 ( FIG. 4 ) generates quantization indexes for each block (8 ⁇ 8 block) by decoding the input code data and outputs the generated quantization indexes for each block to the dequantizing section 50 .
  • Step S 105 the distribution estimating section 520 estimates the distribution of transform coefficients T for each transform coefficient kind, based on the plurality of quantization indexes input from the entropy decoding section 40 .
  • the zero determining section 522 classifies the input quantization indexes into transform coefficient kinds and determines as to whether the classified quantization indexes correspond to the zero transform coefficients or the non-zero transform coefficients.
  • the non-zero transform coefficient distribution estimating section 524 ( FIG. 5 ) prepares the histogram hc(q) of the quantization indexes (that is, the histogram for each transform coefficient kind c) for each group of quantization indexes corresponding to the non-zero transform coefficients and calculates the Laplace function L (that is, values of ⁇ ) approximating the histogram hc(q).
  • the zero transform coefficient distribution estimating section 526 ( FIG. 5 ) approximates the frequency distribution calculated by the non-zero transform coefficient distribution estimating section 524 by an exponential function and estimates the frequency distribution of zero transform coefficients (that is, values of ⁇ ) using this exponential function.
  • Step S 110 the dequantizing section 50 ( FIG. 4 ) sets the input quantization indexes to a given quantization index in order.
  • the dequantization-value estimating section 500 ( FIG. 4 ) extracts neighboring quantization indexes Q(c, i+m, j+n) ( ⁇ 1 ⁇ m ⁇ 1 and ⁇ 1 ⁇ n ⁇ 1 in this example) around the given quantization index Q(c, i, j).
  • the extracted neighboring quantization indexes are quantization indexes of the same transform coefficient kind c in 3 ⁇ 3 blocks around the given block and have a 3 ⁇ 3 matrix.
  • Step S 115 the dequantizing-value estimating section 500 prepares a difference matrix P by performing the following calculation using the extracted neighboring quantization indexes and the given quantization index.
  • P ( m, n ) Q ( c, i+m, j+n ) ⁇ Q ( c, i, j )
  • the dequantizing-value estimating section 500 calculates a difference value between a value of the given quantization index and values of the neighboring quantization indexes.
  • the dequantizing-value estimating section 500 compares an absolute value
  • TH for example, 1
  • Step S 120 the dequantizing section 50 ( FIG. 4 ) determines as to whether or not dequantization values can be estimated for the given quantization index.
  • the dequantizing section 50 determines that the estimation of dequantization values is impossible. Otherwise, the dequantizing section 50 determines that the estimation of dequantization values is possible.
  • Step S 115 If the dequantizing section 50 determines that the estimation of dequantization values (in this embodiment, estimation of the correction factors ⁇ ) is possible, the process proceeds to Step S 115 . If the dequantizing section 50 determines that the estimation of dequantization values is impossible, the process proceeds to Step S 120 .
  • Step S 125 the dequantization-value estimating section 500 calculates correction factors ⁇ ycq, using a 3 ⁇ 3 filter kernel K(m, n) shown in FIG. 10 , by performing a convolution operation for the difference matrix P having been subjected to the threshold process. Accordingly, even when values of the given quantization indexes are equal, if neighboring quantization indexes around the given quantization indexes are different, the calculated correction factors ⁇ ycq have different values.
  • a filter shown in FIG. 10 has a low pass characteristic.
  • Step S 130 the random-number generating section 560 generates random numbers according to the distribution data input from the distribution estimating section 520 for the given quantization index and outputs the generated random numbers to the dequantization-value outputting section 590 as the correction factors ⁇ .
  • the random-number generating section 560 selects a distribution corresponding to the given quantization index from among the distributions estimated by the non-zero transform coefficient distribution estimating section 524 and the zero transform coefficient distribution estimating section 526 , generates random numbers to match the selected distribution, and outputs the generated random numbers to the dequantization-value outputting section 590 as the correction factors ⁇ .
  • Step S 135 the dequantizing section 50 determines as to whether or not the correction factors ⁇ are generated for all quantization indexes. If it is determined that the correction factors ⁇ are generated for all quantization indexes, the process proceeds to Step S 140 . Otherwise, the process returns to Step S 110 where a next quantization index is taken as a given quantization index to be processed.
  • Step S 140 the expected-value estimating section 540 calculates expected values E( ⁇ Tcq) of the probability density function for each combination of the transform coefficient kind and the quantization indexes based on the distribution data input from the distribution estimating section 520 , and outputs the calculated expected values E( ⁇ Tcq) to the correcting section 580 .
  • Step S 145 the correcting section 580 classifies the correction factors ⁇ calculated by the dequantization-value estimating section 500 for each transform coefficient kind and each quantization index, and calculates the minimum value, the maximum value and a mean value of the classified correction factors ⁇ .
  • the correcting section 580 compares the expected values E ( ⁇ Tcq) input from the expected-value estimating section 540 with the calculated mean value for each combination of the transform coefficient kind and the quantization indexes, and shifts a group of correction factors ⁇ ycq classified into combinations of the transform coefficient kind and the quantization indexes such that the expected values E( ⁇ Tcq) become equal to the mean value (shift correction).
  • the correcting section 580 determines as to whether or not the group of correction factors ⁇ having been subjected to the shift correction falls within a range of ⁇ 0.5 to 0.5. If it is determined that the group of correction factors ⁇ does not fall within the range, a range correction to make the range of the group of correction factors ⁇ ycq fall within the range of ⁇ 0.5 to 0.5 is performed without changing the mean value of the group of correction factors ⁇ ycq.
  • Step S 150 the dequantization-value outputting section 590 ( FIG. 4 ) calculates a dequantization value Ry to be applied, based on the given quantization index Q and the correction factors ⁇ input from the correcting section 580 or the correction factors ⁇ input from the random-number generating section 560 , and outputs the calculated dequantization value Ry to the inverse transforming section 60 .
  • the dequantization-value outputting section 590 in this example calculates the dequantization value Ry by performing the following calculation.
  • Ry ( c, i, j ) ⁇ Q ( c, i, j )+ ⁇ ( c, i, j ) ⁇ D ( c )
  • Step S 155 the inverse transforming section 60 ( FIG. 4 ) performs an inverse transform (an inverse DCT in this example) using the dequantization value (approximate transform coefficient) input from the dequantizing section 50 to generate a decode image H.
  • an inverse transform an inverse DCT in this example
  • the dequantization value approximately transform coefficient
  • the decoding apparatus 2 in this embodiment estimates the distribution of transform coefficients based on the quantization indexes, generates the random numbers to match the estimated distribution, and generates the dequantization values based on the generated random numbers.
  • the configuration including the dequantization-value estimating section 500 for calculating the correction factors ⁇ using the neighboring quantization index values and the random-number generating section 560 for generating the random numbers, which matching the distribution of quantization indexes, as the correction factors ⁇ has been described in the above embodiment.
  • the dequantization-value estimating section 500 is not essential. That is, the random-number generating section 560 may generate the correction factors ⁇ for all quantization indexes.
  • the non-zero transform coefficient distribution estimating section 524 makes an estimation by approximating the probability density function by a straight line (polygonal line) connecting ⁇ min, ⁇ mid, and ⁇ max.
  • the non-zero transform coefficient distribution estimating section 524 employs another approximation method. More specifically, the non-zero transform coefficient distribution estimating section 524 alternates between a plurality of approximation methods based on a threshold TH 1 , which is a positive integer. That is, assuming that q is a quantization index value,
  • the first linear approximation may be applied for all values of q.
  • the first and second linear approximations are the polygonal-line approximations as shown in FIG. 11A .
  • the non-zero transform coefficient distribution estimating section 524 estimates values of fk( ⁇ min) and fk( ⁇ max) using neighboring histograms hc(q ⁇ 1) and hc(q+1) shown in FIG. 11A .
  • fk ( ⁇ max) a value of fk ( ⁇ max) is estimated as follows.
  • the non-zero transform coefficient distribution estimating section 524 determines a position of a point A as shown in FIG. 11C .
  • a point internally dividing an interval between hc(q) and hc(q+1) by a ratio of hc(q):hc(q+1) is employed as the position of point A.
  • a value of point A can become sufficiently small when a frequency value hc(q) of the given quantization index is less than a frequency value hc(q+1) of a neighboring quantization index or the frequency value hc(q) of the given quantization index approaches zero.
  • the non-zero transform coefficient distribution estimating section 524 estimates a value of fk( ⁇ mid).
  • shapes of the neighboring histograms are classified into two kinds, which are shown in FIGS. 11D and 11E , respectively.
  • the non-zero transform coefficient distribution estimating section 524 calculates fk( ⁇ mid) satisfying a condition of fk( ⁇ mid)>hc(q) when hc(q) has the maximum value (peak), and calculates fk( ⁇ mid) satisfying a condition of fk( ⁇ mid) ⁇ hc(q) when hc(q) has the minimum value (valley).
  • the non-zero transform coefficient distribution estimating section 524 may transform the above-obtained function fk(x) into the probability density function. That is, the probability density function fcq(x) is as follows:
  • the second linear approximation is a linear approximation applied when
  • TH 1 .
  • the non-zero transform coefficient distribution estimating section 524 calculates fk( ⁇ min) according to the following equation.
  • fk( ⁇ max) and fk( ⁇ mid) by the second linear approximation are calculated in the same manner as the first linear approximation.
  • the non-zero transform coefficient distribution estimating section 524 calculates fcq(x) using three numerical values, that is, fk( ⁇ min), fk( ⁇ max) and fk( ⁇ mid) in the same manner as the first linear approximation.
  • the random numbers are generated for all quantization index values q in the above embodiment.
  • the second modification shows an example where the random numbers are generated for part of the quantization index values q.
  • the dequantization-value estimating section 500 cannot estimate the dequantization values only when all differences between the given quantization index value and the neighboring-quantization index values are 0. Since a number of quantization index values are distributed in 0 as shown in the histogram of FIG. 6 , the possibility that all differences between the given quantization index value and the neighboring quantization index values are 0 as described above becomes high when the given quantization index value is 0.
  • the decoding program 5 in this modification applies the random numbers generated by the random-number generating section 560 as the correction factors ⁇ (or the dequantization values) when the given quantization index value q is 0, and applies the correction factors ⁇ (or the dequantization values) generated by the dequantization-value estimating section 500 when the given quantization index value q is not 0.
  • the random-number generating section 560 generates the random numbers, which match the function fcq(x), in the above embodiment. Random numbers different from the function fcq(x) are generated in the third modification.
  • the function fcq(x) is a function distributed between a range of ⁇ min to ⁇ max. Accordingly, if the quantization step size D(c) is large, a distortion caused when random numbers deviated from the expected value of ⁇ are generated is likely to become large.
  • the third modification limits the range of random numbers as described below.
  • the random-number generating section 560 generates random numbers, which match the following probability density function fcq 1 ( x ).
  • the expected value may be calculated.
  • E( ⁇ Tcq) 0.
  • a range of d is limited such that ⁇ min ⁇ E( ⁇ Tcq) ⁇ d and E( ⁇ Tcq)+d ⁇ max.
  • the above equation is an example of taking a generation probability in the neighborhood as 0 using only a center shape ( ⁇ d to d) of fcq(x). By doing so, since values deviated from the expected value are not output, it is possible to limit a square error.
  • the random-number generating section 560 in the fourth modification generates uniform random numbers. Further, in this modification, for the sake of convenience of description, a variance of the Laplace distribution when the distribution of transform coefficients are estimated by the Laplace distribution and the transform coefficient kind c is estimated by the Laplace distribution is assumed as ⁇ (c).
  • the random-number generating section 560 in this modification generates the random numbers according to the following probability density function fcq 2 ( x ).
  • the probability density function fcq 2 ( x ) is a uniform distribution function in a range of [ ⁇ , ⁇ ].
  • a value ⁇ is set such that a range of [E( ⁇ Tcq) ⁇ , E( ⁇ Tcq)+ ⁇ ] does not exceed [ ⁇ min, ⁇ max]
  • the value ⁇ is a parameter to control disorder of a decoded image. Increase of ⁇ leads to increase of disorder of an image. Decrease of ⁇ leads to decrease of disorder of an image, however, results in an image having visible block distortion.
  • each transform coefficient exists in a frequency domain decomposed as shown in FIG. 12 .
  • ⁇ (x, y) is defined as follows.
  • NL is the number of decomposition levels of a wavelet transform.
  • HL ⁇ (6, 2) ⁇ of a coefficient of ( N ⁇ 1)
  • LH ⁇ (6, 6) ⁇ of a coefficient of ( N ⁇ 1) HH That is, it may be generalized as follows.
  • the above values ⁇ may be standard deviations of simple signals or may be results caused by the estimation of the Laplace distribution as described in the above embodiment. As shown in FIG. 12 , the values a are relatively arranged on an x-y plane around a range on a two-dimensional frequency domain of each transform coefficient.
  • the zero transform coefficient distribution estimating section 526 calculates the values ⁇ corresponding to the zero transform coefficients by approximating the values ⁇ by an exponential function.
  • the values ⁇ are obtained by calculating a standard deviation of the quantization indexes Q(c, i, j) for each quantization coefficient kind c.
  • the decoding program 5 in the second embodiment has a configuration shown in FIG. 4 .
  • the distribution estimating section 520 in the second embodiment estimates ⁇ using an established function F + (x, ⁇ ) or F ⁇ (x, ⁇ ).
  • F + (x, ⁇ ) or F ⁇ (x, ⁇ ) which is an integral function of the Laplace distribution, is expressed by the following equation.
  • a normalized histogram of the quantization indexes q is set as H(q).
  • the standard deviation ⁇ which makes the sum of normalized histograms having a range of the quantization indexes q from ⁇ N to N equal to a corresponding integral value of the Laplace distribution, is obtained.
  • a range of coefficients in which q falls within the range of ⁇ N to N is ⁇ (2N+1)D/2 to (2N+1)D/2 in the JPEG.
  • the distribution estimating section 520 obtains the standard deviation ⁇ using Equation (17).
  • the decoding program 5 sets an appropriate integer N in a second modification.
  • integers a and b are prepared in advance.
  • max ⁇ A, B ⁇ represents a function to output larger one of A and B and min ⁇ A, B ⁇ represents a function to output smaller one of A and B.
  • the minimum value and maximum value of q are assumed as qmin and qmax, respectively.
  • round( ) represents a rounding off process such as rounding-off or rounding out six and larger and disregarding the remaining.
  • FIG. 13 is a diagram illustrating the configuration of the distribution estimating section 520 in the second embodiment in more detail.
  • the distribution estimating section 520 includes a frequency distribution measuring section 532 , a histogram normalizing section 534 , an N value acquiring section 536 and a standard-deviation estimating section 538 .
  • the frequency distribution h(q) represents the number of values of the quantization indexes Q(i), which are q.
  • the frequency distribution measuring section 532 acquires the maximum value qM of the absolute values of the quantization index values q.
  • the histogram normalizing section 534 normalizes the frequency distribution h(q) measured by the frequency distribution measuring section 532 and generates a normalized histogram H(q).
  • the N value acquiring section 536 determines a value of N based on qM acquired by the frequency distribution measuring section 532 . Specifically, the N value acquiring section 536 performs the above-mentioned processes (1) to (3).
  • the standard-deviation estimating section 538 calculates the standard deviation ⁇ based on the value of N acquired by the N value acquiring section 536 , the normalized histogram H(q) generated by the histogram normalizing section 534 , and the quantization step size D input from outside.
  • FIG. 14 shows a relationship between the maximum value of quantization values and the optimal value of N. As shown in FIG. 14 , there is a linear relationship between qM and the optimal value of N.
  • N is obtained using the linear function of qM.
  • qM it is not indispensable to set qM as the maximum value of the absolute values of the quantization indexes.
  • qmax or qmin may be also used as qM.
  • the value of N is obtained by applying the rounding off process using the round ( ) function to an output of the linear function.
  • a rounding-down process or a rounding-out process may be employed in order to obtain the integer value N.
  • the range may be Nmin to Nmax, where Nmin ⁇ 0 and Nmax ⁇ 0.
  • Nmin may be obtained as a function of qmin and Nmax may be obtained as a function of qmax.
  • a third modification estimation is made using a value of N, which makes an accumulated value of H(q) to be a certain value P (0 ⁇ P ⁇ 1). That is, the N value acquiring section 536 in the third modification obtains N by giving a preset value P as expressed by the following equation.
  • the frequency distribution measuring section 532 measures the frequency distribution h(q) based on the input quantization index Q(i).
  • h(q) represents the number of values of quantization indexes Q(i), which are q.
  • the frequency distribution measuring section 532 acquires the maximum value qM of the absolute values of the quantization index values q.
  • the histogram normalizing section 534 generates the normalized histogram H(q) based on the frequency distribution h(q) measured by the frequency distribution measuring section 532 .
  • the N value acquiring section 536 determines the value of N based on the normalized histogram H(q) generated by the histogram normalizing section 534 and qM acquired by the frequency distribution measuring section 532 .
  • the value P is a preset value.
  • the N value acquiring section 536 determines the value of N according to the flow chart as shown in FIG. 15 . Further, qm in the flow chart of FIG. 15 indicates the maximum value (qM) of the absolute values of q. Furthermore, SUM indicates an accumulated value (accumulated frequency) of the frequency value H(q).
  • (S 225 : Yes). Also, the N value acquiring section 536 sets N i ⁇ 1 and terminates the process (S 235 ) if NewSUM ⁇ P (S 220 : Yes) and
  • the N value acquiring section 536 determines the value of N according to the above process.
  • the N value acquiring section 536 outputs the following equation, which is a result of addition of the normalized histogram, to the standard-deviation estimating section 538 .
  • the standard-deviation estimating section 538 calculates the standard deviation ⁇ based on the value of N input from the N value acquiring section 536 , the result of addition of the normalized histogram H(q), and the quantization step size D input from outside.
  • RMSE root mean square error
  • RMSE is 4.176.
  • RMSE is 4.033.
  • the method in this embodiment does not require a numerical calculation as in the conventional technique, and accordingly, can stably perform a high-speed calculation without falling in a local solution.
  • FIG. 16 shows the ratio of the standard deviation of original transform coefficients measured for various images, color components and quantization step sizes to the estimated standard deviation. Since a vertical axis represents a ratio of an estimated standard deviation/a true standard deviation, a ratio approaching 1 indicates a good performance.
  • JP2004-80741A that is, the conventional example
  • the second or third modification is applied when the value of X is large.
  • the distribution estimating section 520 first estimates ⁇ with the same method as the second or third modification, evaluates a value of X using the estimated ⁇ , employs ⁇ estimated according to the method of the conventional example when X is smaller than a preset threshold, and employs ⁇ estimated according to the second or third modification when X is larger than the preset threshold.
  • the distribution estimating section 520 estimates ⁇ using the second or third modification when the maximum value of the quantization indexes (or the maximum value of the absolute values) is smaller than a preset threshold and estimates ⁇ using the method of the conventional example when the maximum value of the quantization indexes (or the maximum value of the absolute values) is larger than the preset threshold.
  • the distribution estimating section 520 may calculate and apply an intermediate value of ⁇ between the value of ⁇ calculated by the method of the conventional example and the value of ⁇ calculated by the second or third modification.
  • the distribution estimating section 520 can integrate these calculation results to take the intermediate value of ⁇ , thereby obtaining a value of ⁇ closer to the actual standard deviation.
  • the distribution estimating section 520 calculates a final standard deviation ⁇ according to the following equation.
  • a constant c is a preset value.
  • RMSE SQRT(a mean value of square of difference between the true standard deviation and the estimated standard deviation) is calculated.
  • SQRT ( ) is a function to calculate a square root.

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